Lyle Ramshaw has authored 5 sequences.
Original entry on oeis.org
6, 30, 140, 631, 2786, 12136, 52368, 224406, 956516, 4060038, 17175132, 72454075, 304941386, 1280898304, 5371301504, 22491017758, 94055344244, 392888085100, 1639534704632, 6835739258998, 28477594607348, 118551827347576
Offset: 0
Lyle Ramshaw (lyle.ramshaw(AT)hp.com), Apr 08 2008
A128941
Cardinality of the free modular lattice generated by two elements and a chain of length n.
Original entry on oeis.org
4, 28, 138, 629, 2784, 12134, 52366, 224404, 956514, 4060036, 17175130, 72454073, 304941384, 1280898302, 5371301502, 22491017756, 94055344242, 392888085098, 1639534704630, 6835739258996, 28477594607346, 118551827347574
Offset: 0
Lyle Ramshaw (lyle.ramshaw(AT)hp.com), Apr 08 2008
When n = 0, the lattice consists of the two elements, their meet and their join, so a(0) = 4.
When n = 1, we get the free modular lattice generated by three elements, so a(1) = 28.
- G. Birkoff, Lattice Theory, American Mathematical Society, third edition (1967), pp. 63-64 [for the case n = 1].
A023813
a(n) = n^(n*(n+1)/2).
Original entry on oeis.org
1, 1, 8, 729, 1048576, 30517578125, 21936950640377856, 459986536544739960976801, 324518553658426726783156020576256, 8727963568087712425891397479476727340041449, 10000000000000000000000000000000000000000000000000000000
Offset: 0
Lyle Ramshaw (ramshaw(AT)pa.dec.com)
A023814
Number of associative binary operations on an n-set; number of labeled semigroups.
Original entry on oeis.org
1, 1, 8, 113, 3492, 183732, 17061118, 7743056064, 148195347518186, 38447365355811944462
Offset: 0
Lyle Ramshaw (ramshaw(AT)pa.dec.com)
- Alex Bailey, Martin Finn-Sell, and Robert Snocken, Subsemigroup, ideal and congruence growth of free semigroups, arXiv preprint arXiv:1409.2444 [math.GR], 2014.
- A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
- C. Noebauer, Home page [broken link]
- C. Noebauer, The Numbers of Small Rings
- C. Noebauer, Thesis on the enumeration of near-rings
- Eric Postpischil Posting to sci.math newsgroup, May 21 1990
- Eric Weisstein's World of Mathematics, Semigroup.
- Index entries for sequences related to semigroups
A023815
Number of binary operations on an n-set that are commutative and associative; labeled commutative semigroups.
Original entry on oeis.org
1, 1, 6, 63, 1140, 30730, 1185072, 66363206, 7150843144, 3829117403448
Offset: 0
Lyle Ramshaw (ramshaw(AT)pa.dec.com)
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